Why is there a size limitation on human/animal growth? Assuming the technology exists for man to grow to 200 feet high, it's pretty much a given that the stress on the skeletal structure and joints wouldn't be possible to support the mass or move...but WHY is this? if our current skeletal structures and joints can support our weight as is, wouldn't a much larger skeletal structure do the same assuming it's growing in proportion with the rest of the body? And why wouldn't a giant person be able to move like normal sized humans do? (I'm honestly thinking Ant Man, or even the non-biological sense of mechs/gundams/jaegers)...I'm just having a hard time grasping why if it were possible to grow to gigantic sizes or create giant robots, why it then wouldn't be possible for them to move.

A quick energy check is that, multiplying scale by $r$, the volume and the weight of the animal are multiplied by $r^3$, so need of food is also multiplied by $r^3$, so daily land area needed is also multiplied by $r^3$, so, certainly, above some $r$, it costs too much energy to feed. See also muscle strengh constraints (being proportionnal to $r^2$) in the link given by Qmechanic.
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TrimokJul 29 '13 at 19:00

8 Answers
8

The following fact lies at the heart of this and many similar issues with sizes of things: Not all physical quantities scale with the same power of linear size.

Some quantities, like mass, go as the cube of your scaling - double every dimension of an animal, and it will weigh eight times as much. Other quantities only go as the square of the scaling. Examples of this latter category include

Muscle strength (a longer muscle can exert no more force than a shorter one of equal cross sectional area),

Heart pumping ability (the heart is not solid but rather hollow, so the amount of muscle powering it goes as the surface area),

The compression/tension that can be safely transmitted by a bone (material strength is intrinsic and independent of size, so the pressure that can be supported is constant, so the force - cross sectional area times pressure - that can be supported goes as the square of size), and

The ability to exchange material and heat the the environment (single cells for example have a hard time growing large because their metabolism goes as the cube of the size, but their ability to transport nutrients across their outer membranes only scales as the area of those membranes),

at least to a first approximation. You could also come up with other quantities that scale differently with size.

As a result, simply scaling up an organism will undo the balance that has been achieved for that particular size. Its muscles will likely be too weak, its bones will likely break, and it will generate so much internal heat (if it is warm blooded) that the only equilibrium achievable given its comparatively small surface area would be at a high enough temperature to denature many proteins.

For a completely non-biological example, consider the fact that airplanes cannot be made arbitrarily large, and in fact different sizes of planes have very different shapes and engineering requirements. The surface area of the wings does not scale the same way as the total mass, and the stresses and pressures the material needs to withstand will not stay constant as you enlarge the plane.

It's worth adding to this that the first person to put these ideas forward was Galileo Galilei, whose book Two New Sciences was concerned both with physical scaling laws and with the work on motion and gravity for which he is more widely remembered today.
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NathanielAug 5 '13 at 9:43

Scaling in three dimensions is much harder, though. The pressure on the bottom is proportional to the height--eventually that pressure is too great for tissue to withstand. (Likewise with many other considerations).

So you could have arbitrarily large essentially 1D or 2D animals (if they had mouths uniformly distributed all over the body). But apparently this isn't very competitive with 3D forms (e.g. it's very hard to hide from predators when you are a giant sheet), so there aren't any longer than a few dozen meters. (There's a 50+ meter long worm, for instance. It has only one mouth, however.)

The basic answer is that mass scales with the cube of linear dimension and strength of things like legs scales with the square of the linear dimension. Note that large animals have therefore evolved comparatively thicker legs than smaller ones. Linearly scale up a dog to elephant size, and its legs would snap. Even more extreme, think of scaling a ant to elephant size.

All this means that the maximum practical size of a moving animal is governed by the strength of the supporting material (bone in our case) relative to the gravity in the environment (1 g in our case). If animals evolved with a similar structural material on a planet with higher gravity, then we'd expect the largest ones to be smaller than here on earth.

The problem can be gotten around to some extent when the animal is floating in water. It's no accident that the largest moving-body animal is aquatic. Eventually other parameters that don't scale the same with linear dimension get in the way, even if supported all around by water.

There were some utter whoppers on land even so: Amphicoelias Fragillimus, a giant sauropod dinosaur was thought to have weighed 120 tonnes and was 60m in length: not too far behind Balaenoptera musculus, the Blue Whale which reaches 170 tonnes and 30m length. The dinosaur Bruhathkayosaurus (another sauropod) may have been considerably heavier even than Amphicoelias, possibly reaching over 200 tonnes.
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WetSavannaAnimal aka Rod VanceAug 30 '13 at 13:34

The straight physics answer to this question - namely "Not all physical quantities scale with the same power of linear size." - is perfectly put by Chris White. This essentially answers your question about giant robots - there are no hard limits, but the scaling power issues simply mean that it gets harder and harder to build bigger and bigger. Modern engineering shows how different this question is when applied to animals. The limits are making themselves felt, but in very different ways for machines as opposed to animals. Take a look at this Krupp coal digging machine used to mine brown (i.e. very wet) coal in the Nordrhein-Westfalen land (the westernmost sticky-out bit of Germany on a map).

The machine is 95 metres high and 215 metres long, weighs forty-six thousand tons and "eats" seventy six thousand cubic metres of coal, stone and earth each day.

Okay, the building materials are very different in machines and animals, but animals have bones whose strength to weight ratio we've only very recently achieved with highly advanced composite materials. So I think it is pretty safe to say that living animals, as opposed to machines, don't even come near to the "physical" limits spoken of in Chris's answer as would apply if living animals had more plentiful resources.

What other limits apply in the case of animals? They are essentially biological, and so this question really needs to be posted as well on biology stack exchange. But they are worth stating here as example of some interesting dynamical system and game theoretic phenomenons - they are an abstract form of Johannes's answer - to wit nimbleness, both physical AND genetic. A good case study here is Amphicoelias Fragillimus, and like, giant sauropod dinosaurs as maybe the biggest creatures, either on land or sea, to ever walk the Earth:

If you get very big, your evolution slows down. It takes a long time to grow up and reproduce. The generation period becomes long. If you think of evolutionary adaptation as a search through configuration space to find ways to adapt to changes around you then the speed of that search is set by the generation period.

"Designing" a Big Animal Machine: Amphicoelias Fragilimus

My drawing below shows the comparative sizes of some sauropod dinosaurs, a human and one of the human's toys, the A380 Airbus. The latter (mainly from being full of air)is only a little bigger than Amphicoelias Fragilimus (the big red-brown, 60m long creature in the background) but their weights are quite comparable (at least when the airbus is unladen). The way Amphicoelias copes with the problem of heat dissipation is spoken about in Rex Kerr's answer, for she is essentially a flat beast, being very narrow when looked at from head on. Maybe her specific name fragilimus refers to this if we take the meaning of slight - I actually don't know where the name comes from. Aside from this, there is of course nothing "fragile" about such a colossal wight.

Now let's look at what Amphicoelias had evolved for. Her food was the hard needle leaves and wood of the coniferous forests of her time - hers was an era before angiosperms: before fruits, flowers and grass. So she needed to be essentially a giant enzyme-catalysed cellulose digesting plant on legs. A humble modern chemical engineer would have no trouble whatsoever in designing and having built a plant of this modest size with fairly mundane (not advanced composite) building materials; the thirty or so tonnes of cellulose in Amphicoelias's maw at a time would be a smaller figure for processing in today's economies-of-scale-obsessed world. The mechanical design and technology needed to make such a plant mobile poses problems that our technology comfortably overcomes. In short, Amphicoelias shows no sign of being up against the physical limits that would limit a giant robot.

Shielding and Defense of The Young, Herd Behaviour and Resource Dearth

No predator of her time, or any before or after, was any threat whatsoever to a the colossal Amphicoelias (at least when healthy): this is one clear evolutionary advantage to being big, although with the sauropods the need for economies of scale in processing a low-grade food source like pine and cycad needles were likely the main drivers towards sheer size.

But the defense of her young was quite a different matter. Baleen whales and Elephants have the same problem today: whilst they themselves are big enough to easily fight any predator (Killer Whale and Lion, respectively) off, their sluggishness is no match for the smaller predator's nimbleness and so their babies are vulnerable. A thirty metre long, one hundred and fifty tonne blue whale has no hope defending her calf against a pod of five tonne killer whales who nimbly dart in, deftly dodging any threat the mother might pose with her tail and worry the hapless young to death unhindered. Their catch can be made in the time it takes the mother merely to turn around. Whales must overcome this problem mainly through their seldomhood - by making themselves scarce and steering clear of where killer whales dwell whenever they are bearing and rearing young. Elephants likewise: their enormous brain (three to four times as big as ours) helps here to work out where lions are and are not likely to be hiding.

For Amphicoelias the problem was even worse. A whale calf is born at several tonnes weight and thus can somewhat defend itself, but dinosaurs hatched from eggs, whose size was limited for reasons given here to about the same size as those of a modern ostrich. Amphicoelias and the sauropods therefore evolved two strategems to compensate for their sluggishness: weapon bluff and herd behavior.

It seems fairly clear from the muscularity, density and shape of a sauropod's tail that the tail was wielded as a fearsome weapon; its muscularity and tough skin show that it could be flicked like a whip, achieving near sonic speeds at its tip. Such a baleful thing hurtling through the air near sonic speeds and with tens or even hundreds of kilograms per metre linear density would clearly be utterly and devastatingly lethal to any living thing it was brought to bear against, and it could be swiftly deployed anywhere in a semicircular region of tens of metres radius near the animal's hinder body. So the weapon partly made up for the sauropod's sluggishness.

But, like most weapons, its worth was mainly as bluff. It is utterly pointless to use such a weapon if your own young are being attacked - and sauropods lacked the keenness of sight needed to deploy a whip with the accuracy needed to avoid hitting one's own young. So the weapon is pretty worthless for a lone creature - hence the next stratagem: herd behavior.

Like elephants today, sauropods were known to live in great herds. Their young could safely graze ringed by their whip bearing parents. But herd behavior and safety in numbers means a huge drain on resources, particularly as individuals get bigger. One Amphicoelias needed to strip one tree each day to live, so here then is the ultimate limit to their size: the sauropods got as big as they could and still have enough to live on. The paper Burness, Diamond and Flannery, "Dinosaurs, dragons, and dwarfs: The evolution of maximal body size" cited by Aufkag shows this: the biggest creatures live on the bountifulest lands.

Genetic Nimbleness

In a sauropod dinosaur's case, the lifespan was estimated at around 200 years and there was only so much room and food for such big animals, so, even though these creatures could lay eggs and beget young quickly, only few lived and the generation period was likely similar to the lifetime, say $10^2$ years. So we come back to the idea of evolutionary adaptation as the finding of ways to adapt to ecological shifts around you by seeking through the genetic configuration space for genotypes better fitted for the shifted conditions. And if you are reproducing slowly, you aren't seeking quickly. Therefore the bigger an animal becomes, the slower its life cycle, the likelier it is to be outdone by its ecological peers who search the genetic configuration space more nimbly, particularly when it lives in herds and is thus precariously dependent on a steady food supply.

If you imaging two species in the same ecological niche, then they should search the genetic configuration space at roughly the same speed, otherwise one will outcompete the other. There is some evidence for this idea in the relative gene combinatorics versus number of individuals in the case of producer prokaryotes and eukaryotes. Prokaryotes evolve by swapping "plasmids" - single genes rolled into a ring that float in the cell's cytoplasm to maybe later insert themselves into the main DNA sequence - one at a time, whereas eukaryotes can reproduce sexually, producing a wholesale genetic mix with each coupling. So producer eukaryotes can test a much bigger range of genotype with each generation and thus do not "fall behind" the much more numerous producer prokaryotes: the two rivals are thus likely searching the genetic configuration space at roughly the same rate.

I'm reading some excellent answers here. One aspect has not received any attention though: survival by agility. Mice are agile, elephants less so. Size definitely plays a role here.

Considering animals utilizing legged locomotion in an environment with gravitational acceleration $g$. The leg height $h$ in combination with the gravitational acceleration defines an 'agility timescale':

$$t_\text{agile} = \sqrt{\frac{h}{g}}.$$

This 'agility timescale' characterizes the time required to turn around or change course. For a human (leg height $h \approx 1~\text{m}$) on earth ($g \approx 10~\text{m/s}^2$), $t_\text{agile} \approx 0.3~\text{s}$. This indeed is a characteristic time for us to turn around.

It probably is no coincidence that evolution has resulted in leopards hunting prey their own size or even larger. Despite the strength that comes with it, size can be a liability. A too large predator, despite its potentially high speed, would fail to catch smaller and more agile prey. And, even worse, it would fall itself prey to groups of smaller and more agile predators.

This ignores that there are advantages to size too. Everything is a careful ballance. Big enough so you don't have to worry about predators (at least once you're full grown) has been tried and found to work. Elephants are a good example, with lions probably provide the evolutionary pressure to get big. Moose in North America is another example. I've seen a film where a single large moose stood off a whole pack of wolves. The wolves eventually gave up because the risk of getting a crushed skull from a flying moose hoof was too great.
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Olin LathropAug 30 '13 at 14:21

@OlinLathrop Good point. But I think Johannes's answer is the nearest to what is limiting animal as opposed to machine size. If you get big, you lack the nimbleness needed to shield your young - then you have to take on other behaviours to make up for your sluggishness - see my answer just written.
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WetSavannaAnimal aka Rod VanceOct 1 '13 at 13:30

A human heart can only pump so fast. At a certain height, the size of the heart will be disproportionate to the size necessary to pump blood throughout the body. If we assume that the heart isn't a problem, bone density is and muscular structure is. You could also think about all the health concerns that relate to obesity and apply them as the relate to overall size. As a giant robot not being able to move, that would just be a problem of torque as it relates to the size a robot's feet must be to ensure its balance. If it were possible to create super lightweight robots, then that wouldn't be a problem. In humans however, cartilage in joints still wears down no matter how much of it there is. A very large human would have terrible joint problems and would destroy most of his joints very early on in his life.

As @ChrisWhite , @Olin etc. have already said, the main issue is that body mass and bone strength (etc.) have different scaling behaviours with respect to the linear dimension of the animal. Mass, being related to volume, grows faster (assuming a "normal shaped" creature) and hence at some point the limbs can't support the animal... especially not if it is expected to be dynamic.

There are also pressure issues with mollusc scaling but as long as they remain underwater these aren't important: the classic example of this being violated by movie physics was in It Came From Beneath The Sea where Ray Harryhausen's giant squid destroys the Golden Gate Bridge. There is a lovely decimation of the physics (and biology) of thie at http://fathom.lib.uchicago.edu/2/21701757/ , concluding that after the creature raises its tentacles high out of the water:

The evidence clearly points to the poor cephalopod suffering a sudden
and massive cerebral hemorrhage from this excess pressure just as it
rips down the Golden Gate Bridge.

You can drop a mouse down a thousand-yard mine shaft; and, on arriving
at the bottom, it gets a slight shock and walks away, provided that
the ground is fairly soft. A rat is killed, a man is broken, a horse
splashes.

Finally, for an entertaining derivation of the absolute scale (rather than the relative scalings of body dimensions), see the paper "The Height of a Giraffe" (http://arxiv.org/abs/0708.0573), summarised in the abstract as:

A minor modification of the arguments of Press and Lightman leads to
an estimate of the height of the tallest running, breathing organism
on a habitable planet as the Bohr radius multiplied by the
three-tenths power of the ratio of the electrical to gravitational
forces between two protons.